1. Equations of Circles
AS Maths with Liz

2. Writing equations of circles in the form
Objectives
Writing equations of circles in the form
Finding the centre and radius of a circle given the equation.

3. The equation of a circle
Standard form is written as
r is the length of the radius
Describes the translation of the centre from the origin from left (+ a) to right (- a)
Describes the translation of the centre from the origin rising (- b) and falling (+ b)
The centre is at the point

4. The Unit Circle
The unit circle is our most basic circle, with centre starting at the origin (0, 0) and radius of 1 unit.
The equation of the unit circle is
Every other circle will be a translation of the unit circle.

5. Example 1 Given the equation of the circle complete the following:
list the radius (c) draw a graph
(b) list the centre

6. Example 2
What is the equation of the circle with centre (-1, -2) and radius 4? Sketch a graph.

7. You try!
Write an equation for the following circles given the centre and radius. Then draw their graphs.
(a) centre (3, -3) and radius 2
(b) centre (4, 2) and radius 5

8. Match each equation to the correct diagram

9. Example 3
Find the centre and radius of the given circle. Hence sketch the curve.
Note: To check your answer, you can always expand your brackets and make sure it comes out to equal what you started with!

10. You try!
Find the centre and radius of the given circle. Hence sketch the curve.
(a)

11. You try!
Find the centre and radius of the given circle. Hence sketch the curve.
(b)

12. Independent Study
Mymaths Equations of Circles online homework Please copy, complete, mark, and correct all questions in your book. Come to drop in if you need support. DUE NEXT LESSON, November 18th.